Quantum Thermalization Breakdown: Localization and Multifractality

12 Oct 2026, 08:45 → 16 Oct 2026, 18:00 Europe/Stockholm

Albano 3: 4205 - SU Conference Room (40 seats) (Albano Building 3)

Ivan Khaymovich (Stockholm University, Nordita)

Venue

Albano campus, Nordita, Stockholm, Sweden

House 3, Floor 4, auditorium 4205
See the campus and Google maps via the links.

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Scope

The workshop provide an up-to-date overview of the latest research in these areas and allow to engage leading experts in the field into the Nordic community.

While numerous previous events focused exclusively on many-body localization, the uniqueness of the proposed workshop is that the main focus is shifted to random-matrix description of ergodicity-breaking phenomena, and especially multifractal phases of matter, and to an effort to find connections between a universal random-matrix description, on one hand, and the model computer simulations and real experiments in many-body systems, on the other. We have identified a rather large recent body of literature developed in the last couple of years, which will form the basis for discussions during this conference, while the more focused character of the workshop will allow for deeper discussions and collaborations between the experts in the field and younger researchers.

 

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Themes and preliminary program schedule

The workshop will have an emphasis on, but not limited to, the following directions:

• Non-ergodic phases of matter (RMT)
• Correlations and non-ergodic dynamics in disordered quantum systems
• Non-Hermitian disordered models
• Many-body localization
• Role of Krylov basis in quantum thermalization
• Free probability and nonstabilizerness frameworks

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Schedule (tentative)

For the full schedule with abstracts and poster session contributions - please see Timetable on the left menu panel or via the above link.

Invited speaker	Date and Time	Talk title
Oct 12		Correlations and non-ergodic dynamics in disordered quantum systems
Organizers	8:45 - 9:00	Opening
Serguei SKIPETROV	9:00 - 10:00	Anderson localization of light
	Coffee break
G. Luca CELARDO	10:30 - 11:30	Shaping causality: programmable nonlocal signal generation in long-range spin systems
Adway Kumar DAS	11:30 - 12:30	Non-ergodic phase of the β ensemble
	Lunch break
Lev VIDMAR	14:00-15:00	Information Compression at Criticality
Maksimilian USOLTCEV	15:00 - 16:00	Theory of Anderson localization on the hyperbolic plane
	Coffee break
All participants	16:30 - 18:00	Discussion
All participants	18:00 - 19:30	Poster session + Reception
Oct 13		Non-ergodic phases of matter in RMT
Anandamohan GHOSH	9:00 - 10:00	Spectral Form Factor in Random Matrix Ensembles
	Coffee break
Peter SOLLICH	10:30 - 11:30	Effects of topological heterogeneity on random matrix spectra
Yan FYODOROV	11:30 - 12:30	Exact spectral solution of a finite-channel random Schrödinger operator: fermionization of the Dyson--Riccati gas
	Lunch break
Leticia CUGLIANDOLO	14:00 - 15:00	Level statistics and multifractality in random matrix ensembles
Marco TARZIA	15:00 - 16:00	Hunting Rare Resonances in Many-Body Localized Phases
	Coffee break
All participants	16:30 - 18:00	Discussion
Oct 14		Non-Hermitian disordered models + Free probability and nonstabilizerness frameworks
Piotr SIERANT	9:00 - 10:00	Nonstabilizerness of ergodic and non-ergodic quantum dynamics
	Coffee break
Elisa VALLINI	10:30 - 11:30	Local Rotational Invariance and Free Probability for refining the Eigenstate Thermalization Hypothesis
Jakub ZAKRZEWSKI	11:30 - 12:30	Quantum Sun and its extensions as models for MBL
	Lunch break
Giuseppe DE TOMASI	14:00 - 15:00	Ergodicity in Hilbert Space: From Porter–Thomas to Entanglement and Quantum Designs
Aleksander GLODKOWSKI	15:00 - 16:00	Anomalously Slow Transport in Tilted Chains
	Coffee break
All participants	16:30 - 18:00	Discussion
Oct 15		Many-body localization
David LUITZ	9:00 - 10:00	Scaling PXP scars
	Coffee break
Henning SCHOMERUS	10:30 - 11:30	Hierarchical expansion approaches to spectral statistics and defect localization
Jens BARDARSON	11:30 - 12:30	Scale-resolved localisation in the information lattice
	Lunch break
Achilleas LAZARIDES	14:00 - 15:00	Some recent results on constrained quantum models
Budhaditya BHATTACHARJEE	15:00 - 16:00	Beyond Gaussianity (Levy SYK)
	Coffee break
All participants	16:30 - 18:00	Discussion
All participants	19:00 - 21:00	Conference dinner in the restaurant "Artilleriet" (menu, how to walk there)
Oct 16		Role of Krylov basis in quantum thermalization
Jerome DUBAIL	9:00 - 10:00	Operator entanglement in random free fermion circuits
	Coffee break
Pawel CAPUTA	10:30 - 11:30	The linear growth of spread complexity
Pratik NANDY	11:30 - 12:30	Designs without disorder: How does a single Hamiltonian generate unitary k-designs?
	Lunch break
Bikram PAIN	14:00 - 15:00	Krylov-space anatomy and spread complexity of a disordered quantum spin chain
Mathias Albert	15:00 - 16:00	Localisation and chaos in one dimensional quantum gases
Organizers	16:00 - 16:15	Closing remarks
All (interested) participants	16:15 - 18:00	Informal Discussion

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Invited speakers

Cugliandolo Leticia	LPTHE, CNRS
Das Adway Kumar	Loughborough University
Ghosh Anandamohan	IISER Kolkata
Solich Peter	University of Goettingen
Tarzia Marco	LPTMC, CNRS
Usoltcev Maksimilian	University of Cologne

 

Celardo G. Luca	University of Florence
Pain Bikram	ICTS / UT Austin
Skipetrov Sergei	LPMMC CNRS
Vidmar Lev	Institut "Jožef Stefan"
Zakrzewski Jakub	Jagiellonian University

 

De Tomasi Giuseppe	IST CEFMA, University of Lisbon
Dubail Jerome	ISIS, CNRS
Fyodorov Yan	KCL
Shomerus Henning	Lancaster University

 

Albert Mathias	INPHYNI, CNRS
Bardarson Jens	KTH
Glodkowski Aleksander	Wroclaw University of Science and Technology
Lazarides Achilleas	Loughborough University
Luitz David	University of Bonn

 

Bhattacharjee Budhaditya	University of Luxembourg
Caputa Pawel	Stockholm University
Nandy Pratik	Vrije University Brussels

 

Sierant Piotr	Barcelona Supercomputing Center
Vallini Elisa	University of Cologne

 

 

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Accommodation

Accommodation for invited speakers will be organized and paid by Nordita in BizApartments in Stockholm area.
The contributed speakers should pay accommodation themselves.
Nordita can provide the BizApartments for the reduced rate by the request (please see the application form). 

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Travel support

Due to the limited budget, no travel support is possible. 

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Application/Registration

Registration (please see the application form) to be considered for on-site participation will close August 10, 2026. Registrants will receive an on-site/remote participation confirmation from the organizers after this date.

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Sponsored by:

10_MTarzia_IPR-corrections.pdf

11_PSierant_SlidesMagic.pdf

12_EVallini_Slides Stockholm 14.10.26.pdf

13_JZakrzewski_nord26.pdf

14_GDeTomasi_Sto.pdf

15_AGlodkowski_Nordita_Stark_Chain.pdf

17_HSchomerus_Stockholm_2026.pdf

18_JBardarson_the information lattice seminar.pdf

19_ALazarides_stockholm-slides.key_.pdf

1_SSkipetrov_al_light_nordita.pdf

20_BBhattacharjee_nordita-talk-BB-2026.pdf

21_JDubail_Stockholm2026.pdf

23_PNandy_Nordita_talk.pdf

24_BPain_Krylov-Space-NORDITA-.pdf

25_MAlbert_NORDITA_2026.pdf

2_GLCelardo_NORDITA-2026_.pdf

3_AdwayKDas_10_26_Nordita.pdf

4_LVidmar_Talk Nordita.pdf

5_MUsoltcev_main.pdf

6_AGhosh_SFF_Nordita 2.pdf

7_PSollich_Degree_heterogeneity.pdf

8_YFyodorov_Riccati-talk.pdf

9_LCugliandolo_Stockholm26.pdf

Monday 12 October

1 Opening remarks

Speaker: Prof. Ivan Khaymovich (Stockholm University, Nordita)

2 Anderson localization of light

All waves – quantum or classical, mechanical or electromagnetic – often behave in a similar way. It turns out, however, that electromagnetic waves in general and light in particular are very different from other types of waves when propagation in strongly disordered media is concerned. Whereas matter, acoustic or elastic waves experience Anderson localization in any space dimension (and, in particular, in 3D), this phenomenon is notoriously difficult to realize for light in 3D. Experimental reports existing for 30 years have been continuously questioned. Theoretical studies indicate that longitudinal electromagnetic fields may be an obstacle for Anderson localization. Only very recently we have been able to capitalize on previous theoretical studies to design an experiment in which Anderson localization of light in 3D has been observed. In this talk, I will review the exciting research that led to this recent success.

Speaker: Dr Serguei Skipetrov (LPMMC)

Slides

10:00 Coffee break

3 Shaping causality: programmable nonlocal signal generation in long-range spin systems

Understanding how information spreads in non-relativistic many-body systems is a central issue for quantum information processing. While short-range interactions confine information within a local light cone, long-range interactions typically lead to uncontrolled nonlocal spread across the entire system. Here, we demonstrate that this apparent dichotomy is not fundamental, and that the onset of nonlocality in systems with long-range interactions can be deterministically controlled. By mapping spin dynamics to a hard-core boson chain, we identify a regime where the causal space-time landscape can be precisely shaped. We show that placing spin excitations in a polarized background allows a local perturbation to trigger nonlocal signals exactly at the positions of these excitations. These pre-selected sites act as seeds for new, effective light cones, allowing information to bypass the bulk and re-emerge at distant, programmable locations. This mechanism avoids uncontrollable global nonlocality while circumventing the speed limits associated with local transport. By engineering these nonlocal communication channels, our findings offer a versatile framework for information distribution relevant to quantum memories, error correction, and programmable platforms such as trapped ions.

Speaker: Prof. Giuseppe Luca Celardo (University of Florence)

Slides

4 Non-ergodic phase of the β ensemble

In random matrix theory, the β ensemble is a generalization of the Wigner-Dyson ensembles to arbitrary values of β. Dumitriu and Edelman proposed a matrix model of the β ensemble, which is equivalent to a single-particle Hamiltonian with inhomogeneous disorder in the hopping amplitudes. The β ensemble exhibits a non-ergodic phase which has many distinctive features: weak long-range energy correlation despite the absence of short-range correlation, coexistence of localized and extended states without forming any mobility edge, fast eqiulibration of quench dynamics. All these anomalous properties can be understood from a spatially local equivalence to the 1D Anderson model. In the zero temperature limit (β → ∞), the β ensemble reduces to a deterministic Hamiltonian, which has an energy-coordinate duality to the quantum Harmonic oscillator. We find that corresponding bulk states have energy dependent multifractality.

Speaker: Dr Adway Kumar Das (Loughborough University)

Slides

12:30 Lunch break

5 Information Compression at Criticality

Speaker: Prof. Lev Vidmar (Institut "Jožef Stefan")

Slides

6 Theory of Anderson localization on the hyperbolic plane

The two-dimensional hyperbolic plane, H^2, is an unusual system in that dimensionality changes with scale: locally two-dimensional and planar at short distances, but effectively infinite-dimensional at large scales, it provides an interesting paradigm for the study of (quantum) phase transitions, notably the disorder-driven Anderson transition. Generalizing previous work, which treated short and large distance scales separately, we develop a unified framework interpolating between the principles of low- and high-dimensional Anderson localization. As a main result, we derive a two-parameter flow in a plane spanned by scale-dependent curvature (setting the system's effective dimensionality) and conductivity, with an extended critical line separating metallic and insulating phases.

Speaker: Dr Maksimilian Usoltcev (University of Cologne)

Slides

16:00 Coffee break

7 Topical Discussion

Poster session + reception

8 Out-of-time-order correlators with Symmetry Resolution

We extend the concept of operator charge in the context of an abelian U (1) symmetry and apply this framework to symmetry-preserving matrix product operators (MPOs), enabling the description of operators projected onto specific sectors of the corresponding symmetry. Leveraging this representation, we study the effect of interactions on the scrambling of information in an integrable Heisenberg spin chain, by controlling the number of particles. Our focus lies on out-of-time order correlators (OTOCs) which we project on sectors with a fixed number of particles. This allows us to link the non-interacting system to the fully-interacting one by allowing more and more particle to interact with each other, keeping the interaction parameter fixed. The spreading of the information front becomes gradually faster and the OTOC saturate at larger values as the number of particle increases. We also study the behavior of finite-size systems by considering the OTOCs at times beyond the point where the front hits the boundary of the system. We find that in every sector with more than one particle, the OTOCs behave as if the local operator was rotated by a random unitary matrix, indicating that the presence of boundaries contributes to the maximal scrambling of local operators.

Speaker: Martina GISTI (University of Bonn)

9 Post-measurement Quantum Monte Carlo

We show how the effects of large numbers of measurements on many-body quantum ground and thermal states can be studied using Quantum Monte Carlo (QMC). Density matrices generated by measurement in this setting feature products of many local nonunitary operators, and by expanding these density matrices as sums over operator strings we arrive at a generalized stochastic series expansion (SSE). Our `post-measurement SSE' is based on importance sampling of operator strings contributing to a measured thermal density matrix. We demonstrate our algorithm by probing the effects of measurements on the spin-$1/2$ Heisenberg antiferromagnet on the square lattice. Thermal states of this system have \SU{2} symmetry, and at first we preserve this symmetry by measuring \SU{2} symmetric observables. We identify classes of post-measurement states for which correlations can be calculated efficiently, as well as states for which \SU{2} symmetric measurements generate a QMC sign problem when working in any site-local basis. For the first class, we show how deterministic loop updates can be leveraged. Using our algorithm we demonstrate the creation of long-range Bell pairs and symmetry-protected topological order, as well as the measurement-induced enhancement of antiferromagnetic correlations. We then study the effects of measuring the system in a basis where the standard (unmeasured) SSE is sign-free: For measurement schemes with this property, we can calculate correlations in all post-measurement states without a sign problem. The method developed in this work opens the door to scalable experimental probes of measurement-induced collective phenomena, which require numerical estimates for the effects of measurements.

Speaker: Kriti BAWEJA (University of Bonn)

10 Renyi Negativity from Nonequilibrium Work

We develop a Quantum Monte Carlo method based on the Replica trick in order to calculate Renyi Negativities of any order. These quantities serve as multipartite and mixed state Entanglement measures. This method has been succesful in estimating Entanglement Entropies and is extended to Renyi Negativities. Subjecting the replicas to a non equilibrium protocol transforming their configuration according to the structure of their respective partially transposed density matrices, the estimator is obtained by applying a fluctuation-dissipation theorem known as Jarzynskis equality, relating the performed mechanical work to the Free energy. This is implemented on the basis of the Stochastic Series Expansion algorithm which is benchmarked on the dimerized Heisenberg model. Investigated near the Groundstate the model exhibits a quantum critical transition.

Speaker: Jannis KASTELL (University of Bonn)

11 Anomalous and Conventional Mobility Edges in Quasiperiodic ABF Diamond Chain

Mobility edges (MEs) that separate localized, multifractal, and ergodic states in energy are a central concept in understanding Anderson localization. In this work, we study the effect of an additional constant offset on the mobility-edge formation in the one-dimensional all-bands-flat (ABF) diamond chain with a quasiperiodic potential. We show that this offset can transform anomalous mobility edges (AMEs), i.e., boundaries separating localized and multifractal states, into conventional mobility edges separating localized and ergodic states. We further compare the numerically obtained ME structure with an analytical estimate motivated by Avila’s global theory. While the estimate provides useful insight into the mobility-edge formation, discrepancies with the numerical results appear both at a quantitative level, through shifts in the mobilityedge locations, and at a qualitative level, through the emergence of multiple mobility edges not captured by the analytical estimate.

Speaker: Manish Kumar (IISER Bhopal)

12 Exact solution of the forward-scattering chain in the PXP model

The PXP chain is the standard example of weak ergodicity breaking: a Neel product state fails to thermalise, returning periodically for long times, and the return is attributed to a tower of nearly equally spaced eigenstates. How nearly equally spaced they are, and whether the resulting revivals survive in the thermodynamic limit, has not been settled. We solve the forward-scattering approximation, the standard analytic model of that tower, exactly. The hopping amplitudes of the forward-scattering chain, previously available only numerically, are obtained in closed form, and their deviation from a perfect SU(2) multiplet is computed analytically in the thermodynamic limit. It converges to a fixed profile rather than vanishing, so the tower is not an SU(2) multiplet at any system size. This does not, however, spoil the revivals. The Neel state occupies only a narrow central window of the tower, where the level spacings are uniform to order 1/L, and the revival fidelity within the forward-scattering subspace approaches unity as the chain grows. Since the true PXP revivals decay with system size, the anharmonicity of the tower cannot be what limits scarring.

Speaker: Dr Saurav PANDEY (Ben Gurion University of the Negev)

13 Measurement-induced crossover of quantum jump statistics in postselection-free many-body dynamics

Open quantum systems under measurement have now been extensively studied because they exhibit interesting nonequilibrium dynamics absent in isolated quantum systems. Of particular interest is the physics of quantum trajectories, where one tracks the monitored dynamics with the measurement outcomes (i.e., quantum jumps) retained. Indeed, such quantum trajectories concerning many-body systems can exhibit interesting phenomena represented as measurement-induced phase transitions (MIPT), which cannot be obtained by the dynamics where measurement outcomes are averaged. However, the MIPT generally requires the postselection of the same quantum measurement outcomes, which causes experimentally unfriendly exponential cost. Our work shows a nontrivial crossover of subsystem fluctuations of quantum jumps in many-body dynamics, which does not require the aforementioned postselection problem because quantum jumps are directly obtained in a single quantum trajectory. Whereas the fluctuations show the conventional volume law (∼ L) following Poissonian statistics for sufficiently weak measurement strength, anomalous universal scaling law (∼ L^2.7 up to L=20) exhibiting super-Poissonian statistics appears for strong measurement strength. We also discuss that this crossover significantly affects the precision of estimating the rate of quantum jumps. That is, for strong (weak) measurement, the estimation uncertainty is enhanced (suppressed) as the system size increases. Moreover, we demonstrate that the obtained anomalous scaling of the subsystem fluctuation results from an integrated many-body autocorrelation function. We can access the measurement-induced crossover only through the postselection-free information, i.e., the time and the position of quantum jumps, which can be tested in ultracold atom experiments.

Speaker: Prof. Kazuki YAMAMOTO (Osaka Metropolitan Uni)

14 Restricted typicality in non-equilibrium quantum many-body systems

Macroscopic conservation laws fundamentally bottleneck the time evolution of isolated quantum many-body states. We demonstrate that time-evolved states in ergodic disordered models act as typical states drawn from an instantaneous Scrooge ensemble $\rho(t)$—an ensemble that maximizes randomness subject to restriction on local charge profiles. Analytical predictions from this framework excellently match exact unitary evolution, revealing that the complex growth of entanglement and participation entropies is fundamentally restricted by underlying hydrodynamics. Furthermore, extending this approach to integrable systems reproduces the results of generalized hydrodynamics, explicitly recovering the quasiparticle picture formula for entanglement entropy growth following inhomogeneous quantum quenches.

Speaker: Konrad PAWLIK (Jagiellonian University)

15 Fragmentation in non-Hermitian models

I will present how different spin-1 models give rise to various types of fragmentation. The key to understanding when complex versus real spectra emerge is the interplay between the range and type of interactions. Interestingly, I will also present a toy model demonstrating how a complex spectrum can be mapped onto a system with open boundaries, despite the model itself having periodic boundaries.

Speaker: Maria ZELENAYOVA (Stockholm University)

16 Persistent coherent quantum dynamics in 2D long-range magnets via magnon binding

State-of-the-art quantum simulation platforms, such as those in Rydberg atomic systems or trapped ions, are inherently long-range interacting, yet little is known about how their unique excitations govern out-of-equilibrium dynamics in two dimensions. Numerically simulating this real-time evolution in 2D, however, poses a serious computational bottleneck. In this Letter, we overcome these challenges by deploying large-scale neural quantum state simulations together with analytical effective theory to investigate the post-quench dynamics of the 2D transverse-field Ising model with power-law decaying interactions. We discover that the system exhibits remarkably long-lived coherent oscillations and slow relaxation. To unveil the underlying physics, we develop an effective quasiparticle theory demonstrating that the long-range tail binds distant magnons into highly stable composite states that arrest thermalization. By systematically tuning the power-law exponent , we map the precise crossover from long-range bound-state dominance to the short-range limit where these excitations dissolve. Finally, we demonstrate that this magnon bound states picture is a generic, robust feature of 2D long-range quantum magnets, providing a universal framework to understand and exploit persistent quantum coherence in current experimental setups.

Speaker: Vighnesh Dattatraya NAIK (University of Augsburg)

17 Krylov Complexity: A New Order Parameter?

Krylov complexity - a measure of operator growth through Heisenberg time evolution via the Lanczos-constructed Krylov basis - has proven useful as a probe of quantum chaos and dynamical phase transitions, but we ask whether it can also detect topological phase transitions, motivated by the fact that both the change in level statistics and the change in underlying geometry accompanying such transitions should leave an imprint on the Krylov construction. We test this on two toy models: the Kitaev chain, where we compute K-complexity for the circuit connecting the free-fermion and Kitaev ground states across the topological/trivial phase boundary using a BdG diagonalization and su(2,ℂ) coherent-state formalism; and a pair of linearly coupled Bateman oscillators, where K-complexity resolves the onset of the PT-symmetric regime. Our results suggest Krylov complexity is a computationally tractable order parameter for topological phase transitions, extending its role beyond chaos diagnostics into ground-state topology.

Speaker: Dr Nitin GUPTA (Jagiellonian University)

18 Non-ergodic dynamics from chiral symmetries

We demonstrate strong non-ergodic behavior in the XY model on coupled chains, where domain-wall initial states retain an inhomogeneous magnetization profile for arbitrarily long times. We find that this effect arises due to zero modes protected by chiral symmetry. Using an analysis based on the Lanczos algorithm, we identify evidence for a localization transition in the thermodynamic limit at a critical coupling between the chains. We further show that antiferromagnetic defects in the initial state and symmetry-breaking perturbations restore slow thermalization, whereas it remains robust for symmetry-conserving perturbations. These results establish that degenerate, symmetry-protected subspaces can give rise to thermodynamically stable non-ergodic dynamics in experimentally accessible quantum systems [1].

[1] P. Kos, D. S. Wild, and K. Knakkergaard Nielsen, arXiv:2604.15510 (accepted for publication in Phys. Rev. Letters).

Speaker: Dr Kristian Knakkergaard NIELSEN (Niels Bohr Institute, University of Copenhagen)

Tuesday 13 October

19 Spectral Form Factor in Random Matrix Ensembles

We study the spectral properties of a tridiagonal matrix ensemble that is isospectral to random matrices, in which strength of level repulsion (β) can be tuned continuously to interpolate between integrable and chaotic regimes. Our analysis reveals that the spatial inhomogeneity in the β-ensemble gives rise to Non-Ergodic Extended (NEE) states and is devoid of any mobility edge. This NEE phase is associated with an unconventional energy scale which is captured by the Spectral Form Factors (SFF). The relaxation dynamics in β-ensemble is significantly different from those observed in standard many-body systems. Furthermore, using finite temperature spectral form factors we systematically probe distinct energy scales and extract the system-size scaling laws of the associated relaxation times.

Speaker: Prof. Anandamohan Ghosh (IISER Kolkata)

Slides

10:00 Coffee break

20 Effects of topological heterogeneity on random matrix spectra

Speaker: Prof. Peter Sollich (University of Goettingen)

Slides

21 Exact spectral solution of a finite-channel random Schr\"odinger operator: fermionization of the Dyson--Riccati gas

We solve exactly, for arbitrary finite channel number $N$, the Riccati dynamics of a quasi-one-dimensional random matrix Schr""odinger operator with Hermitian white-noise potential in the unitary symmetry class.
At $\beta=2$, the associated Dyson--Riccati gas admits an exact free-fermion representation, yielding explicit finite-$N$ expressions for the density of states and the total Lyapunov growth rate. Equivalently, these quantities are encoded by a Kontsevich matrix Airy $\tau$-function. We then discuss the large-$N$ spectral edge, where the finite-channel Lifshitz-type tail rounds the sharp $N=\infty$ edge within an $N^{-4/5}$ scaling window governed by a universal cubic-oscillator problem. Finally, we discuss a conjectured connection between this scaling regime and the localized spectral edge of a broad class of one-dimensional random band matrices.
The talk is based on joint work in progress with Pierre Le Doussal.

Speaker: Prof. Yan Fyodorov (King's College London)

Slides

12:30 Lunch break

22 Level statistics and multifractality in random matrix ensembles

Speaker: Prof. Leticia Cugliandolo (LPTHE CNRS)

Slides

23 Hunting Rare Resonances in Many-Body Localized Phases

Rare system-wide resonances are expected to play a prominent role in driving the many-body localization (MBL) transition and dictating the stability of the MBL phase. In this talk, we introduce a novel theoretical framework based on an analogy with mean-field disordered glassy systems to properly account for the statistical weight of these resonant configurations. Utilizing this framework, we generate biased disorder realizations to investigate the structural origin of long-range resonances in the Hilbert space. Our results demonstrate that their formation is fundamentally driven by the emergence of extended regions with anomalously weak disorder in real space.

Speaker: Dr Marco Tarzia (LPTMC CNRS)

Slides

16:00 Coffee break

24 Topical Discussion

Wednesday 14 October

25 Nonstabilizerness of ergodic and non-ergodic quantum dynamics

Magic state resources, also known as the non-stabilizerness, quantify the beyond-Clifford operations necessary for universal quantum computing and are related to complexity of representing states of quantum many-body systems on classical computers. How rapidly are magic resources generated by generic many-body dynamics under constraints of locality? What can we say about non-stabilizerness of time-evolved state in the limit of long-time evolution under many-body Hamiltonians? In this talk, I will address these questions by discussing non-stabilizerness of Haar-random states, and its relation with non-stabilizerness of eigenstates of ergodic many-body systems [1]. Subsequently, I will discuss the problem of magic spreading in brick-wall random unitary circuits [2], which combine principles of locality and unitarity, serving as a minimal model of ergodic many-body dynamics. This model shows that magic resources equilibrate on timescales logarithmic in system size N, akin to Hilbert space delocalization measures, but differently from entanglement entropy. I will discuss how this results extend to ergodic [3] and many-body localized [4] systems.
[1] X. Turkeshi, A. Dymarsky, P. Sierant, Phys. Rev. B 111, 054301 (2025)
[2] X. Turkeshi, E. Tirrito, P. Sierant, Nat Commun 16, 2575 (2025)
[3] E. Tirrito, X. Turkeshi, P. Sierant, Phys. Rev. Lett. 135, 220401 (2025)
[4] P. R. Nicácio Falcão, P. Sierant, J. Zakrzewski, E. Tirrito

Speaker: Dr Piotr Sierant (Barcelona Supercomputing Center)

Slides

10:00 Coffee break

26 Local Rotational Invariance and Free Probability for refining the Eigenstate Thermalization Hypothesis

Understanding how isolated quantum many-body systems reach thermal equilibrium is a central question in nonequilibrium physics. The Eigenstate Thermalization Hypothesis (ETH) provides a powerful framework by linking thermalization to the statistical properties of matrix elements of physical observables in the energy eigenbasis. In this talk I will present a recent work in which we revisit and clarify in detail the ideas that have led to the formulation of full ETH, a generalization of the ETH ansatz that captures multi-point correlation functions. Specifically, using tools from free probability, we explore the implications of local rotational invariance, a property that emerges from the statistical invariance of observables under random basis transformations induced by small perturbations of the Hamiltonian. This approach allows us to analytically characterize subleading corrections to matrix-element correlations, thereby refining the ETH ansatz. Our results open several promising directions for future research in many-body quantum dynamics as well as in quantum information theory.

Speaker: Elisa Vallini (University of Cologne)

Slides

27 Quantum Sun and its extensions as models for MBL

I will discuss the Quantum Sun model as an example of 0-dimensional model exhibiting MBL. We introduce the interacting Anderson Quantum Sun model, which significantly deviates from the conventional expectations. In addition to standard localized and ergodic phases, we identify a regime that exhibits volume-law entanglement coexisting with intermediate spectral statistics. We also identify another nonstandard regime marked by Poisson level statistics, sub-volume entanglement growth, and rare-event-dominated correlations, indicative of emerging ergodic instabilities. The talk will be based on Phys. Rev. B113, L180203 (2026).

Speaker: Prof. Jakub Zakrzewski (Jagiellonian University)

Slides

12:30 Lunch break

28 Ergodicity in Hilbert Space: From Porter–Thomas to Entanglement and Quantum Designs

Thermalization is intimately connected to ergodicity in Hilbert space, namely the spreading of the wave function over the many-body Fock space, which links quantum dynamics to random matrix theory.
First, I will discuss the self-dual kicked Ising model, a minimal model of many-body quantum chaos, and show how an initially localized state converges to a Haar-random state with Porter–Thomas statistics. Second, I will show that entanglement entropies can be fully ergodic even when the wave function occupies only a vanishing fraction of the Hilbert space.
Finally, I will ask whether ergodicity can be defined independently of the observable. Using quantum k-designs and their frame potential, I will show that fractal states look Haar-random at the level of k moments only when their fractal dimension is large enough.

Speaker: Prof. Giuseppe De Tomasi (IST CEFMA, University of Lisbon)

Slides

29 Anomalously Slow Transport in Tilted Chains

Speaker: Aleksander Głódkowski (WUST/LPT CNRS)

Slides

16:00 Coffee break

30 Topical Discussion

Thursday 15 October

31 Scaling PXP scars

Do the quantum many-body scars of the PXP model survive in the thermodynamic
limit? Polynomial filter diagonalization gives access to exact eigenstates at the
center of the spectrum for long chains. I will present new results
on the energies, entanglement and Néel-state overlap of the scar states up to L=40.

Speaker: Prof. David Luitz (University of Bonn)

10:00 Coffee break

32 Hierarchical expansion approaches to spectral statistics and defect localization

I report on three different expansion approaches that systematically capture spatial and dynamical content of complex wave functions.
The first approach uses the surface Green's function to analyze and design interface and defect states at any arbitrary energy [1].
The second approach expands the dynamical correlations of generalized spectral form factors in ergodic stochastic systems [2,3].
The third approach expands the resolvent Green's function in terms of modes of the adjugate matrix, which provides detailed insights into spectral deficient scenarios [4,5,6].

[1] Renormalization approach to the analysis and design of Hermitian and non-Hermitian interfaces, H. Schomerus, Phys. Rev. Res 5, 043224 (2023).
[2] Hierarchical analytical approach to universal spectral correlations in Brownian quantum chaos, T. Kalsi, A. Romito, and H. Schomerus, Phys. Rev. B 111, 094211 (2025).
[3] Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling, T. Kalsi, A. Romito, and H. Schomerus, Quantum 9, arXiv:2310.11355 (2025).
[4] Eigenvalue sensitivity from eigenstate geometry near and beyond arbitrary-order exceptional points, H. Schomerus, Phys. Rev. Res. 6, 013044 (2024).
[5] Fragmented exceptional points and their bulk and edge realizations in lattice models, S. Bid and H. Schomerus, Phys. Rev. B 112, 195433 (2025).
[6] Uniform response theory of non-Hermitian systems: Non-Hermitian physics beyond the exceptional point, S. Bid and H. Schomerus, Phys. Rev. Res. 7, 023062 (2025).

Speaker: Prof. Henning Schomerus (Lancaster University)

Slides

33 Scale-resolved localisation in the information lattice

I will explain how to use the information lattice to extract universal information about localisation in many-body states.

Speaker: Jens H Bardarson (Department of Theoretical Physics, KTH Royal Institute of Technology, Stockholm)

Slides

12:30 Lunch break

34 Some recent results on constrained quantum models

I will present some recent results on constrained many-body models, focussing on East-type and PXP-type models.

Speaker: Prof. Achilleas Lazarides (Loughborough University)

Slides

35 Beyond Gaussianity (Levy SYK)

Gaussian disorder is used to descibe several chaotic and non-integrable properties of quantum many-body systems. Most other disorders lead to similar physical properties (especially for large systems with many degrees of freedom) due central limit effects. Going beyond Gaussian (and central limit) disorders provides an avenue for exploring physics outside Gaussian universality. Focus on uncorrelated disorder, I will present a strongly correlated quantum many body model of fermions with non-central-limit disorder. This will allow us to explore several non-Gaussian properties, such as non-maximal chaos in an otherwise maximally chaotic systems. I will also discuss a solvable limit of this model, and analyses of spectral and dynamical chaos in that. Finally, I will demonstrate emergent non-fermi liquid and spin-glass effects arising due to the disorder modification, without any structural changes in the system.

Speaker: Dr Budhaditya Bhattacharjee (University of Luxembourg)

Slides

16:00 Coffee break

36 Topical Discussion

19:00 Conference dinner

restaurant "Artilleriet"

Friday 16 October

37 Operator entanglement in random free fermion circuits

Speaker: Dr Jerome Dubail (ISIS, CNRS)

Slides

10:00 Coffee break

38 The linear growth of spread complexity

I will discuss aspects of the linear growth of complexity that have motivated the study of complexity measures in high-energy theory. I will then consider a precise notion of quantum complexity, known as spread complexity, and discuss how it exhibits linear growth. I will also illustrate some of the mechanisms underlying this growth and its termination in specific examples.

Speaker: Pawel Caputa (Stockholm University)

39 Designs without disorder: How does a single Hamiltonian generate unitary k-designs?

Unitary k-designs efficiently reproduce Haar-random statistics up to the k-th moment. In this talk, we show that Hamiltonian randomness is not required: a single chaotic Hamiltonian, including deterministic local systems, can generate approximate unitary k-designs. We introduce a two-Pauli-kick (2PK) protocol, where evolution under one fixed Hamiltonian is interspersed with two Pauli kicks, with randomness arising solely from the evolution times. The resulting frame potential approaches the Haar value at long times, with finite-size deviations suppressed by the inverse Hilbert-space dimension. We demonstrate this mechanism analytically and numerically for a single realisation of random matrices, SYK models, and deterministic local quantum spin chains, establishing a simple route to unitary designs without Hamiltonian disorder.

Speaker: Dr Pratik Nandy (Vrije University Brussels)

Slides

12:30 Lunch break

40 Krylov-space anatomy and spread complexity of a disordered quantum spin chain

We investigate the anatomy and complexity of quantum states in Krylov space, in the ergodic and many-body localized (MBL) phases of a disordered, interacting spin chain. The Krylov basis generated by the Hamiltonian from an initial state provides a representation in which the spread of the time-evolving state constitutes a basis-optimized measure of complexity. We show that the long-time Krylov spread complexity sharply distinguishes the two phases. In the ergodic regime, the infinite-time complexity scales linearly with the Fock-space dimension, indicating that the state spreads over a finite fraction of the Krylov chain. By contrast, it grows sublinearly in the MBL regime, implying that the long-time state occupies only a vanishing fraction of the chain. Further, the profile of the infinite-time state along the Krylov chain exhibits a stretched-exponential decay in the MBL regime. This behavior reflects a broad distribution of decay length scales, associated with different eigenstates contributing to the long-time state. Consistently, a large-deviation analysis of the statistics of eigenstate spread complexities shows that while the ergodic regime receives contributions from almost all eigenstates, the complexity in the MBL regime is dominated by a vanishing fraction of eigenstates, which have anomalously large complexity relative to the typical ones.

Speaker: Bikram Pain (ICTS)

Slides

41 Localisation and chaos in one dimensional quantum gases

Understanding the emergence of transport and chaos in interacting quantum systems remains a central challenge in non-equilibrium statistical physics. In this talk, I will present recent results obtained in one-dimensional Bose gases, focusing on two complementary aspects of quantum dynamics: localization and chaos. First, I will discuss dynamical localization in periodically driven Lieb-Liniger gases. While localization persists in both the non-interacting and strongly interacting limits, finite interactions can induce a transition from a localized to a delocalized regime above a critical driving strength. This phenomenon can be understood through an exact mapping onto effective Anderson models in synthetic dimensions generated by the particle number. I will further show how combining interactions with quasiperiodic driving provides a versatile route to engineer Anderson models in arbitrary dimensions and investigate their localization transitions. In the second part, I will turn to quantum chaos in one-dimensional Bose gases. By introducing a localized impurity that breaks integrability, we uncover an unconventional form of diffraction-induced chaos characterized by random-matrix spectral statistics emerging at low energies. These results highlight the rich interplay between interactions, disorder, integrability, and chaos in low-dimensional quantum systems.

Speaker: Prof. Mathias Albert (Institut de Physique de Nice - Université Côte d'Azur)

Slides

42 Closing remarks

Speaker: Prof. Ivan Khaymovich (Stockholm University, Nordita)

43 Informal Discussions